Squeeze enough juice from clementines to measure 1 cup.
Whisk together juice, sugar, cornstarch, and salt in a small heavy saucepan. Bring to a boil over medium heat, whisking constantly, then briskly simmer, whisking, 1 minute.
Remove pan from heat and whisk in butter until melted.
Pour into a bowl and cover surface with wax paper or parchment. Cool to warm, about 30 minutes.
•Sauce can be made 3 days ahead and chilled, covered. Rewarm over low heat before serving.